A car with a dripping gas tank travels along a road in a straight line. A drop falls from the gas tank every five second and over a section of road the spots from the gasoline can be used to determine the motion of the car. From the examples shown below, assuming that the car starts from rest at the location of the first spot on the left, the motion(s) representing constant acceleration is (are)
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Sol. [A] Only pattern 1 represents constant acceleration. From equation (i), since both the initial position and initial velocity are zero, the motion on the car determined by 
…(i).
The distance the car travels is proportional to the square of the elapsed time. For the first 5 second time segment, if the car has traveled 2 meters, at the end of the second 5 second time segment, the car must have traveled 2 2 × 2 meters or 8 meters. At the end of the third 5 second time segment, the car must have traveled 3 2 × 2 meters of 18 meters, and so on. Pattern 2 does not represent distance that is proportional to the square of the elapsed time. Pattern 3 represents a constant acceleration of zero from the second spot on. However, recall that the car started from rest at the position of the first spot and its acceleration was therefore not zero when it traveled from the first to the second spot.
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